I'm following Griffiths' Introduction to Quantum Mechanics, where he's discussing the general solution to the delta-function potential problem. The solution he refers to is $$\psi(x)=Ae^{ikx}+Be^{-ikx}$$

Now, he says that neither of the the terms blows up. The case he is dealing with is $x<0$. I cannot see this, because it seems to me that the second term blows up if $x$ is negative. I suspect he is using some argument that involves the complex nature of the terms. I would like to know if indeed this is the case. If so, what is the argument to show that the terms do not blow up? Thanks.